Work

Embedding Borel graphs into grids of asymptotically optimal dimension

Year: 2026

Type: article

Abstract: Let G G be a Borel graph all of whose finite subgraphs embed into the d d /dimensional grid with diagonals. We show that then G G itself admits a Borel embedding into the Schreier graph of a free Borel action of Z O ( d ) \mathbb {Z}^{O(d)} . This strengthens an earlier result of the authors, in which O ( d ) O(d) is replaced by O ( ρ log ⁡ ρ ) O(\rho \log \rho ) , where ρ \rho is the polynomial growth rate of G G .

Source: Proceedings of the American Mathematical Society

DOI: 10.1090/proc/17597

Authors: Anton Bernshteyn, Jing Yu

Institutions: University of California, Los Angeles, Fudan University

Language: English

Topic: Advanced Topology and Set Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, Alfred P. Sloan Foundation, National Natural Science Foundation of China, China Postdoctoral Science Foundation

Awards: G1164146103, CAREER: Developing a unified theory of descriptive combinatorics and local algorithms, G6671297155, G7152429830, G7808841721